Rewrite as a simplified fraction. ${2.\overline{10} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 210.101...\\ 1x &= 2.101...\end{align*}}$ Subtracting the two equations, we have: ${99x = 208}$ ${x = \dfrac{208}{99}} \text{or} {2 \dfrac{10}{99}}$